Yes, in a web browser you have to log in your account at lightroom.adobe.com. You can then set the collection to custom order, which will then be reflected on the iPad as well. You can drag and drop images to reorder them in the browser, and these changes will be synced to the desktop.

After a bit more playing.... In a collection, tap the three dots in the top right. It looks like the menu text is misleading when it says Sort by Capture Time. It is actually a combination of "Sort by" and whatever the current sort order may be, so Sort by (currently Capture Time). It actually opens up to a menu, including Custom.